Di Natale, who has backtracked on plans to retire, opened his account in the 19th minute, then added another 10 minutes later and completed his hat-trick two minutes before halftime.
Serie A topscorer in 2009/10 and 2010/11, both for Udinese, Di Natale added a fourth in the 75th minute before Cyril Thereau completed the scoring from a penalty in Udinese coach Andrea Stramaccioni's first competitive game in charge.
Fabio Ceravolo replied for the Serie B side in the 34th minute.
Brazilian Eder scored a hat-trick to help Sampdoria beat Como 4-1 in another of Sunday's third round ties and Germany forward Miroslav Klose was among the scores in Lazio's 7-0 demolition of Bassano, where all the goals came in the second half.
(Writing by Brian Homewood in Berne, editing by Pritha Sarkar)
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